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Year 2015, Volume: 3 Issue: 2, 54 - 57, 30.10.2015
https://doi.org/10.36753/mathenot.421331

Abstract

References

  • [1] Aktaş, R., Çekim, B. and C¸ evik, A., Extended Jacobi matrix polynomials. Util. Math. 92 (2013), 47-64.
  • [2] Altın, A. and Çekim, B., Generating matrix functions for Chebyshev matrix polynomials of the second kind. Hacet. J. Math. Stat. 41 (2012), no. 1, 25–32.
  • [3] Altın, A. and Çekim, B., Some properties associated with Hermite matrix polynomials. Util. Math. 88 (2012), 171-181.
  • [4] Batahan, R.S., A new extension of Hermite matrix polynomials and its applications. Linear Algebra Appl. 419 (2006), 82–92.
  • [5] Çekim, B., New kinds of matrix polynomials. Miskolc Math. Notes 14 (2013), no. 3, 817-826.
  • [6] Çekim, B. and Altın, A., New matrix formulas for Laguerre matrix polynomials. Journal of Classical Analysis 3 (2013), no. 1, 59-67.
  • [7] Çekim, B., Altın, A. and Akta¸s, R., Some relations satisfied by orthogonal matrix polynomials. Hacet. J. Math. Stat. 40 (2011), no. 2, 241-253.
  • [8]Çevik, A., Multivariable construction of extended Jacobi matrix polynomials. J. Inequal. Spec. Funct. 4 (2013), no. 3, 6-21.
  • [9] Defez, E. and Jodar, L., Some applications of the Hermite matrix polynomials series expansions. J. Comp. Appl. Math. 99 (1998), 105-117.
  • [10] Defez, E. and Jodar, L., Chebyshev matrix polynomials and second order matrix differential equations. Util. Math. 61 (2002), 107-123.
  • [11] Defez, E., Jodar, L. and Law, A., Jacobi matrix differential equation, polynomial solutions and their properties. Comput. Math. Appl. 48 (2004), 789-803.
  • [12] Defez, E., Jodar, L., Law, A. and Ponsoda, E., Three-term recurrences and matrix orthogonal polynomials. Util. Math. 57 (2000), 129-146.
  • [13] Defez, E., Hervas, A., Law, A., Villanueva-Oller, J. and Villanueva, R.J., Progressive transmission of images: PC-based computations, using orthogonal matrix polynomials. Mathl. Comput. Modelling 32 (2000), 1125-1140.
  • [14] Dunford, N. and Schwartz, J., Linear Operators. Vol. I, Interscience, New York, 1957.
  • [15] Grünbaum, F.A., Pacharoni, I. and Tirao, J.A., Matrix valued orthogonal polynomials of the Jacobi type. Indag. Math. (N.S.) 14 (2003), no. 3-4, 353-366.
  • [16] Jodar, L. and Company, R., Hermite matrix polynomials and second order matrix differential equations. J. Approx. Theory Appl. 12 (1996), no. 2, 20-30.
  • [17] Jodar, L., Company, R. and Navarro, E., Laguerre matrix polynomials and systems of second order differential equations. Appl. Num. Math. 15 (1994), 53-63.
  • [18] Jodar, L., Company, R. and Ponsoda, E., Orthogonal matrix polynomials and systems of second order differential equations. Differ. Equ. Dyn. Syst. 3 (1995), no.3, 269-288.
  • [19] Jodar, L. and Cort´es, J.C., Closed form general solution of the hypergeometric matrix differential equation. Math. Comput. Modelling 32 (2000), 1017-1028.
  • [20] Jodar, L. and Defez, E., A connection between Laguerre’s and Hermite’s matrix polynomials. Appl. Math. Lett. 11 (1998), no. 1, 13-17.
  • [21] Jodar, L. and Sastre, J., On Laguerre matrix polynomials. Util. Math. 53 (1998), 37-48.
  • [22] Sayyed, K.A.M., Metwally, M.S. and Batahan, R.S., On generalized Hermite matrix polynomials. Electron. J. Linear Algebra 10 (2003), 272-279.
  • [23] Sayyed, K.A.M., Metwally, M.S. and Batahan, R.S., Gegenbauer matrix polynomials and second order matrix differential equations. Divulg. Mat. 12 (2004), 101-115.
  • [24] Taşdelen, F., Çekim, B. and Aktaş, R., On a multivariable extension of Jacobi matrix polynomials. Comput. Math. Appl. 61 (2011), no. 9, 2412-2423.

A NOTE ON LAGUERRE MATRIX POLYNOMIALS

Year 2015, Volume: 3 Issue: 2, 54 - 57, 30.10.2015
https://doi.org/10.36753/mathenot.421331

Abstract

In this paper, some new relations for Laguerre matrix polynomials
are given.

References

  • [1] Aktaş, R., Çekim, B. and C¸ evik, A., Extended Jacobi matrix polynomials. Util. Math. 92 (2013), 47-64.
  • [2] Altın, A. and Çekim, B., Generating matrix functions for Chebyshev matrix polynomials of the second kind. Hacet. J. Math. Stat. 41 (2012), no. 1, 25–32.
  • [3] Altın, A. and Çekim, B., Some properties associated with Hermite matrix polynomials. Util. Math. 88 (2012), 171-181.
  • [4] Batahan, R.S., A new extension of Hermite matrix polynomials and its applications. Linear Algebra Appl. 419 (2006), 82–92.
  • [5] Çekim, B., New kinds of matrix polynomials. Miskolc Math. Notes 14 (2013), no. 3, 817-826.
  • [6] Çekim, B. and Altın, A., New matrix formulas for Laguerre matrix polynomials. Journal of Classical Analysis 3 (2013), no. 1, 59-67.
  • [7] Çekim, B., Altın, A. and Akta¸s, R., Some relations satisfied by orthogonal matrix polynomials. Hacet. J. Math. Stat. 40 (2011), no. 2, 241-253.
  • [8]Çevik, A., Multivariable construction of extended Jacobi matrix polynomials. J. Inequal. Spec. Funct. 4 (2013), no. 3, 6-21.
  • [9] Defez, E. and Jodar, L., Some applications of the Hermite matrix polynomials series expansions. J. Comp. Appl. Math. 99 (1998), 105-117.
  • [10] Defez, E. and Jodar, L., Chebyshev matrix polynomials and second order matrix differential equations. Util. Math. 61 (2002), 107-123.
  • [11] Defez, E., Jodar, L. and Law, A., Jacobi matrix differential equation, polynomial solutions and their properties. Comput. Math. Appl. 48 (2004), 789-803.
  • [12] Defez, E., Jodar, L., Law, A. and Ponsoda, E., Three-term recurrences and matrix orthogonal polynomials. Util. Math. 57 (2000), 129-146.
  • [13] Defez, E., Hervas, A., Law, A., Villanueva-Oller, J. and Villanueva, R.J., Progressive transmission of images: PC-based computations, using orthogonal matrix polynomials. Mathl. Comput. Modelling 32 (2000), 1125-1140.
  • [14] Dunford, N. and Schwartz, J., Linear Operators. Vol. I, Interscience, New York, 1957.
  • [15] Grünbaum, F.A., Pacharoni, I. and Tirao, J.A., Matrix valued orthogonal polynomials of the Jacobi type. Indag. Math. (N.S.) 14 (2003), no. 3-4, 353-366.
  • [16] Jodar, L. and Company, R., Hermite matrix polynomials and second order matrix differential equations. J. Approx. Theory Appl. 12 (1996), no. 2, 20-30.
  • [17] Jodar, L., Company, R. and Navarro, E., Laguerre matrix polynomials and systems of second order differential equations. Appl. Num. Math. 15 (1994), 53-63.
  • [18] Jodar, L., Company, R. and Ponsoda, E., Orthogonal matrix polynomials and systems of second order differential equations. Differ. Equ. Dyn. Syst. 3 (1995), no.3, 269-288.
  • [19] Jodar, L. and Cort´es, J.C., Closed form general solution of the hypergeometric matrix differential equation. Math. Comput. Modelling 32 (2000), 1017-1028.
  • [20] Jodar, L. and Defez, E., A connection between Laguerre’s and Hermite’s matrix polynomials. Appl. Math. Lett. 11 (1998), no. 1, 13-17.
  • [21] Jodar, L. and Sastre, J., On Laguerre matrix polynomials. Util. Math. 53 (1998), 37-48.
  • [22] Sayyed, K.A.M., Metwally, M.S. and Batahan, R.S., On generalized Hermite matrix polynomials. Electron. J. Linear Algebra 10 (2003), 272-279.
  • [23] Sayyed, K.A.M., Metwally, M.S. and Batahan, R.S., Gegenbauer matrix polynomials and second order matrix differential equations. Divulg. Mat. 12 (2004), 101-115.
  • [24] Taşdelen, F., Çekim, B. and Aktaş, R., On a multivariable extension of Jacobi matrix polynomials. Comput. Math. Appl. 61 (2011), no. 9, 2412-2423.
There are 24 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ali Çevik

Abdullah Altın This is me

Publication Date October 30, 2015
Submission Date April 17, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Çevik, A., & Altın, A. (2015). A NOTE ON LAGUERRE MATRIX POLYNOMIALS. Mathematical Sciences and Applications E-Notes, 3(2), 54-57. https://doi.org/10.36753/mathenot.421331
AMA Çevik A, Altın A. A NOTE ON LAGUERRE MATRIX POLYNOMIALS. Math. Sci. Appl. E-Notes. October 2015;3(2):54-57. doi:10.36753/mathenot.421331
Chicago Çevik, Ali, and Abdullah Altın. “A NOTE ON LAGUERRE MATRIX POLYNOMIALS”. Mathematical Sciences and Applications E-Notes 3, no. 2 (October 2015): 54-57. https://doi.org/10.36753/mathenot.421331.
EndNote Çevik A, Altın A (October 1, 2015) A NOTE ON LAGUERRE MATRIX POLYNOMIALS. Mathematical Sciences and Applications E-Notes 3 2 54–57.
IEEE A. Çevik and A. Altın, “A NOTE ON LAGUERRE MATRIX POLYNOMIALS”, Math. Sci. Appl. E-Notes, vol. 3, no. 2, pp. 54–57, 2015, doi: 10.36753/mathenot.421331.
ISNAD Çevik, Ali - Altın, Abdullah. “A NOTE ON LAGUERRE MATRIX POLYNOMIALS”. Mathematical Sciences and Applications E-Notes 3/2 (October 2015), 54-57. https://doi.org/10.36753/mathenot.421331.
JAMA Çevik A, Altın A. A NOTE ON LAGUERRE MATRIX POLYNOMIALS. Math. Sci. Appl. E-Notes. 2015;3:54–57.
MLA Çevik, Ali and Abdullah Altın. “A NOTE ON LAGUERRE MATRIX POLYNOMIALS”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 2, 2015, pp. 54-57, doi:10.36753/mathenot.421331.
Vancouver Çevik A, Altın A. A NOTE ON LAGUERRE MATRIX POLYNOMIALS. Math. Sci. Appl. E-Notes. 2015;3(2):54-7.

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